Arrangements of hyperplanes and Lie algebra homology
type: Item
instance of: scholarly article
title: Arrangements of hyperplanes and Lie algebra homology
zbMATH Open document ID: 0754.17024
DOI: 10.1007/BF01243909
published in: Inventiones Mathematicae
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/143938
review text: The authors investigate the cohomology of one-dimensional local systems over complements of hyperplanes in complex affine subspaces. The main results of the paper consist of the study of ``discriminantal'' arrangements. The cohomology of certain local systems over them is closely connected with homology of nilpotent subalgebras of Kac-Moody type Lie bialgebras. Under certain conditions, the complete set of solutions of the Knizhnik-Zamolodchikov differential equations in terms of generalized hypergeometric integrals are given.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B55
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 59798
zbMATH Keywords: cohomology of local systems
zbMATH Keywords: Orlik-Solomon algebra
zbMATH Keywords: flag complex
zbMATH Keywords: discriminantal arrangements
zbMATH Keywords: complements of hyperplanes
zbMATH Keywords: complex affine subspaces
zbMATH Keywords: homology
zbMATH Keywords: Knizhnik-Zamolodchikov differential equations
zbMATH Keywords: generalized hypergeometric integrals
Wikidata QID: Q55920493
author: Vadim Schechtman
author: A. Varchenko
reviewed by: Eugen Pascu
MaRDI profile type: Publication
cites work: Un théorème du type de Matsushima-Murakami concernant l'intégrale des fonctions multiformes
cites work: On the homology of geometric lattices
cites work: HYPERGEOMETRIC-TYPE INTEGRALS AND THE $\mathfrak{sl}(2, {\rm C})$ KNIZHNIK-ZAMOLODCHIKOV EQUATION
cites work: Poisson symmetry algebras and the asymptotics of spectral series
cites work: Moduln mit einem höchsten Gewicht
cites work: Q3693672
cites work: Current algebras and Wess-Zumino model in two dimensions
cites work: Lie algebra cohomology and the generalized Borel-Weil theorem
cites work: An application of Aomoto-Gelfand hypergeometric functions to the SU(n) Knizhnik-Zamolodchikov equation
cites work: Combinatorics and topology of complements of hyperplanes
cites work: Hypergeometric solutions of Knizhnik-Zamolodchikov equations
cites work: Canonical factorization of continuous operator functions relative to the circle
cites work: Q3470717
description: scientific article; zbMATH DE number 59798